Note that the logarithmic Laplacian has the same structure of Dirichlet eigenvalues and eigenfunctions as the fractional Laplacian, see [1]} (cf. also [2]}). A remarkable relationship between the first Dirichlet eigenvalue of
\(L_{\text{\tiny $\Delta \,$}}\!\)  and \((-\Delta )^s\)  for \(s>0\)  close to 0 is given by Theorem REF , which we prove now and restate here for the reader's convenience.
